4. Technological Interest
• The global market for nanomagnetic materials and devices will
rise at an AAGR (average annual growth rate) of 22.6% from $4.3
billion in 2004 to reach nearly $12.0 billion in 2009.
• Information storage applications account for the vast majority –
over 90% – of today’s market and will continue to dominate in
2009.
Source:
Mindy Rittner, Ph.D.
GB-293 Nanomagnetics: Materials, Devices and Markets
Published December 2004
BCC, Inc.,
25 Van Zant St.,
Norwalk, CT 06855
Colossal Magnetoresistance
Why the interest?
5. Fundamental Physics Interest
• The strong coupling of magnetic properties to the lattice
structure, spin ordering, angular momentum ordering, and
charge ordering.
• Complex phase transitions between metallic, ferromagnetic
paramagnetic and insulator phases
• Easily tuned by changing the element concentrations
• Shares complexities with some high temperature
superconductors
Colossal Magnetoresistance
Why the interest?
The theory is still incomplete, however.
7. Mn Fe Co Ni Cu Zn Ga Ge As Se Br KrSc Ti V CrK
Tc Ru Rh Pd Ag Cd In Sn Sb Te I XeY Zr Nb MoRb
Re Os Ir Pt Au Hg Tl Pb Bi Po At RnHf Ta WCs
Bh Hs Mt Uun Uuu UubRf Db SgFr
Na
Li
H
ArClSPSiAl
ON NeFCB
He
Am Cm Bk Cf Es Fm Md No LrPa U Np PuAc Th
Eu Gd Tb Dy Ho Er Tm Yb LuPr Nd Pm SmLa Ce
Ca
Sr
Ba
Ra
Mg
Be
3d Transition Metal Oxides
Mixed-Valence Perovskite Manganese Oxides: R1-xAxMnO3
Colossal Magnetoresistance
Materials
9. C.M. Resistance
Colossal Magnetoresistance
Causal Forces
A little change destroys the effect
Orbital Ordering
Charge Ordering
Spin Ordering
Structural Order
Temperature
Double Exchange
J-T Distortions
15. Colossal Magnetoresistance
Hund’s Rules
• Breaking the Degeneracy
– Hund’s Rules for Multi-electron atomic systems
1. Term with maximum multiplicity lies lowest in energy (spin-spin
coupling) Typically, the largest total S.
2. For a given multiplicity, the term with the largest value of L lies
lowest in energy. (orbit-orbit coupling)
3. For atoms with less than half-filled shells, the level with lowest
value of J lies lowest in energy. (spin-orbit Coupling )
SpinSpaceTotal χψψ =
These rules stem from the overriding constraint of the
Fermi-Dirac statistics on the total probability density function
17. Breaking the Degeneracy in
Many Electron Atomic Systems
ψψ
πεπε
E
r
e
r
Ze
m
N
i ji ijoio
i =
+
−∇−∑ ∑= >1
22
2
2
442
Central Field Approximation
Attractive Repulsive
10 HHH +=
ψψ EH =
∑∑
∑
+−=
+∇−=
< i
i
ioji ijo
i
ii
rU
r
Ze
r
e
H
rU
m
h
H
)(
44
)(
2
22
1
2
2
0
πεπε
Nucleus
Electrons
Colossal Magnetoresistance
Electrons Reside in
Degenerate Energy Levels
18. Spin-Orbit interactions
∑ ⋅=
i
iii SLrH
)(2 ξ
relativistic correction
210 HHHH ++=
Total Hamiltonian
i
i
i
i
dr
rdV
rcm
r
)(1
2
1
)( 22
=ξ
Colossal Magnetoresistance
21 HH >>(i)
21 HH <<(ii)
L-S (or Russell-Saunders) coupling case:
small and intermediate Z
j-j coupling case: large Z
Breaking the Degeneracy in
Many Electron Atomic Systems
22. Colossal Magnetoresistance
Jahn-Teller Distortion
The Jahn-Teller Theorem
was published in 1937 and states:
"any non-linear molecular system
in a degenerate electronic state
will be unstable and will undergo
distortion to form a system of lower
symmetry and lower energy thereby
removing the degeneracy"
23. Colossal Magnetoresistance
J-T Distortions and Further Splitting
Triplet
Doublet
eg
t2g
Jahn –
Teller
Mn3+
Hund’s
Rules
Degeneracy is Split . . . . And with it comes a structural distortion
24. Colossal Magnetoresistance
Orbital Ordering Resulting from Distortions
The ordering of the overall lattice is magnified by the
preferred symmetry and orientation of the individual
electronic orbitals
27. Colossal Magnetoresistance
Implications for Industry
Smaller Storage Devices
100 GB/inch2
now
EMR promises > 1 TB/inch2
Low Power
Reliable and Sustainable
Companies such as IBM, NEC and NVE
have commercial devices on the market
Extraordinary MR
